# The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The determinant of matrix AB is 200 when the determinant of matrix A is 5 and the determinant of matrix B is 40. The detailed solution to find the determinant of matrix A is 5 and the determinant of matrix B is given below.

### Steps to find the determinant of matrix AB

When the determinant of matrix A is 5 and the determinant of matrix B is 40, the determinant of matrix AB can be found in the following ways:

• Let A and B are the square matrix of size ‘n’ then:
• determinant of (A).determinant  of (B) = determinant  of (A.B)
• We know that: the determinant of A is 5 and the determinant of B is 40
• determinant of (A.B) = determinant of (A).determinant of (B) = 5 × 40
• Therefore, determinant (AB) = 200

Summary:

## The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is?

When the determinant of the A matrix is 5 and the determinant of the B matrix is 40 then the determinant of the AB matrix will be 200. The step-by-step process to find the determinant of A and B has been illustrated above.

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